RT Journal Article
T1 Robust inference for non-destructive one-shot device testing under step-stress model with exponential lifetimes
A1 Balakrishnan, Narayanaswamy
A1 Castilla González, Elena María
A1 Jaenada Malagón, María
A1 Pardo Llorente, Leandro
AB One-shot devices analysis involves an extreme case of interval censoring, wherein one can only know whether the failure time is either before or after the test time. Some kind of one-shot devices do not get destroyed when tested, and so can continue within the experiment, providing extra information for inference, if they did not fail before an inspection time. In addition, their reliability can be rapidly estimated via accelerated life tests (ALTs) by running the tests at varying and higher stress levels than working conditions. In particular, step-stress tests allow the experimenter to increase the stress levels at pre-fixed times gradually during the life-testing experiment. The cumulative exposure model is commonly assumed for step-stress models, relating the lifetime distribution of units at one stress level to the lifetime distributions at preceding stress levels. In this paper, we develop robust estimators and Z-type test statistics based on the density power divergence (DPD) for testing linear null hypothesis for non-destructive one-shot devices under the step-stress ALTs with exponential lifetime distribution. We study asymptotic and robustness properties of the estimators and test statistics, yielding point estimation and conffidence intervals for different lifetime characteristic such as reliability, distribution quantiles and mean lifetime of the devices. A simulation study is carried out to assess the performance of the methods of inference developed here and some real-life data sets are analyzed ffinally for illustrative purpose.
YR 2022
FD 2022
LK https://hdl.handle.net/20.500.14352/71929
UL https://hdl.handle.net/20.500.14352/71929
LA eng
NO [1] Balakrishnan, N. (2009). A synthesis of exact inferential results for exponential step-stress modelsand associated optimal accelerated life-tests. Metrika, 69(2), 351-396.[2] Balakrishnan, N. & Castilla, E. (2021) EM-based likelihood inference for one-shot device testdata under log-normal lifetimes and the optimal design of a CSALT plan. Quality and ReliabilityEngineering International, DOI: 10.1002/qre.3014[3] Balakrishnan, N., Castilla, E., Martin, N., & Pardo, L. (2019a). Robust estimators and teststatistics for one-shot device testing under the exponential distribution. IEEE Transactions onInformation Theory, 65(5), 3080-3096.[4] Balakrishnan, N., Castilla, E., Martin, N., & Pardo, L. (2019b). Robust estimators for one-shotdevice testing data under gamma lifetime model with an application to a tumor toxicologicaldata. Metrika, 82(8), 991-1019.[5] Balakrishnan, N., Castilla, E., Martín N. & Pardo, L. (2020a). Robust inference for one-shot devicetesting data under exponential lifetime model with multiple stresses. Quality and ReliabilityEngineering International, 36, 1916{1930.[6] Balakrishnan, N., Castilla, E., Martin, N., & Pardo, L. (2020b). Robust inference for one-shotdevice testing data under Weibull lifetime model. IEEE Transactions on Reliability, 69(3), 937-953.[7] Balakrishnan, N., Castilla, E. & Pardo, L. (2021). Robust statistical inference for one-shot devicesbased on density power divergences: An overview. In B. C. Arnold et al. (eds.), Methodology and Applications of Statistics-A Volume in Honor of C.R. Rao on the Occasion of his 100th Birthday, Springer, New York.[8] Balakrishnan, N. & Ling, M. H. (2012). Multiple-stress model for one-shot device testing data under exponential distribution, IEEE IEEE Transactions on Reliability, 61(3), 809-821.[9] Balakrishnan N. & Ling M.H. (2013). Expectation maximization algorithm for one shot deviceaccelerated life testing with Weibull lifetimes, and variable parameters over stress. IEEE Transactionson Reliability, 62(2), 537{551.[10] Balakrishnan N. & Ling M.H (2014). Gamma lifetimes and one-shot device testing analysis.Reliability Engineering and Systems Safety, 126, 54{64.[11] Balakrishnan, N., Ling, M. H., & So, H. Y. (2021). Accelerated Life Testing of One-shot Devices:Data Collection and Analysis. John Wiley & Sons, Hoboken, New Jersey.[12] Basak, S., Basu, A., & Jones, M. C. (2021). On the \optimal" density power divergence tuningparameter. Journal of Applied Statistics, 48(3), 536-556.[13] Basu, A., Harris, I. R., Hjort, N. L., & Jones, M. C. (1998). Robust and e�cient estimation byminimising a density power divergence. Biometrika, 85(3), 549-559.[14] Basu, A., Mandal, A., Martin, N., & Pardo, L. (2018). Testing composite hypothesis based onthe density power divergence. Sankhya B, 80(2), 222-262.[15] Cramer, H. (1946). Mathematical Methods of Statistics, Princeton University Press, Princeton,New Jersey.[16] Basu, A., Ghosh, A., Mart��n, N., & Pardo, L. (2021). A robust generalization of the Rao test.Journal of Business & Economic Statistics. 1-12.[17] Fan, T. H., Balakrishnan, N., & Chang, C. C. (2009). The Bayesian approach for highly reliableelectro-explosive devices using one-shot device testing. Journal of Statistical Computation andSimulation, 79(9), 1143-1154.[18] Fraser, D. A. S. (1957). Nonparametric Methods in Statistics. John Wiley & Sons, New York.[19] Ghosh, A. (2015). Inuence function analysis of the restricted minimum divergence estimators:A general form. Electronic Journal of Statistics, 9(1), 1017-1040.[20] Lee, C., & Bae, S. J. (2020). Optimal design of accelerated life tests for one-shot devices. In2020 Asia-Paci�c International Symposium on Advanced Reliability and Maintenance Modeling(APARM) (pp. 1-4). IEEE.[21] Hampel, F.R., Ronchetti, E., Rousseeuw, P.J., & Stahel, W. (1986). Robust Statistics: TheApproach Based on Inuence Functions John Wiley & Sons, New York.[22] Ling, M. (2019). Optimal design of simple step-stress accelerated life tests for one-shot devicesunder exponential distributions. Probability in the Engineering and Informational Sciences, 33(1),121-135.[23] Ling, M. H., & Hu, X. W. (2020). Optimal design of simple step-stress accelerated life tests forone-shot devices under Weibull distributions. Reliability Engineering and System Safety, 193, 106630.[24] Meeter, C. A., & Meeker, W. Q. (1994). Optimum accelerated life tests with a nonconstant scaleparameter. Technometrics, 36(1), 71-83.[25] Meeker, W. Q., Escobar, L. A., & Lu, C. J. (1998). Accelerated degradation tests: modeling andanalysis. Technometrics, 40(2), 89{99.[26] Mun, B. M., Sun, E. J., & Bae, S. J. (2013). Bayesian reliability estimation for small sample-sizedone-shot devices. Journal of Applied Reliability, 13(2), 99-107.[27] Nelson, W. (1980). Accelerated life testing-step-stress models and data analyses. IEEE transactionson Reliability, 29(2), 103-108.[28] Newby, M. (2008). Monitoring and maintenance of spares and one shot devices. Reliability Engineeringand System Safety, 93(4):588{594.[29] Olwell, D. and Sorell, A. (2001). Warranty calculations for missiles with only current-status data,using Bayesian methods. In Annual Reliability and Maintainability Symposium: 2001 Proceedings. International Symposium on Product Quality and Integrity (Cat. No. 01CH37179), pages 133{138. IEEE.[30] Sering, R. J. (2009). Approximation Theorems of Mathematical Statistics. John Wiley & Sons, New York.[31] Sharma, R., & Upadhyay, K. (2018). A hierarchical Bayes analysis for one-shot device testing experiment under the assumption of exponentiality. Communications in Statistics - Simulation and Computation, 47(5):1297{314.[32] Viveros, R. & Balakrishnan, N. (1993). Statistical Inference from Start-Up Demonstration Test Data. Journal of Quality Technology, 25(2), 119-130.[33] Wang, R. H., & Fei, H. L. (2003). Uniqueness of the maximum likelihood estimate of the Weibull distribution tampered failure rate model. Communications in Statistics-Theory and Methods, 32(12), 2321-2338.[34] Warwick, J., & Jones, M. C. (2005). Choosing a robustness tuning parameter. Journal of StatisticalComputation and Simulation, 75(7), 581-588.[35] Wu, S. J., Hsu, C. C., & Huang, S. R. (2020). Optimal designs and reliability sampling plans for one-shot devices with cost considerations. Reliability Engineering and System Safety, 197, 106795.[36] Zhu, Y. (2010). Optimal design and equivalency of accelerated life testing plans. PhD Thesis, Rutgers The State University of New Jersey, New Brunswick.[37] Zhu, X., Liu, K., He, M., & Balakrishnan, N. (2021). Reliability estimation for one-shot devices under cyclic accelerated life-testing. Reliability Engineering and System Safety, 212, 107595.
DS Docta Complutense
RD 4 mar 2024